## OVERVIEW

This course focuses on quantum electrodynamics (QED) and it studies its fundamental properties, underlying similarities and differences with other quantum field theories that describe the fundamental interactions in the Standard Model, such as QCD and the electro-weak theory.

## AIMS AND CONTENT

LEARNING OUTCOMES

In this course, we study radiative corrections in quantum field theory, which is the theoretical tool that allows us to arrive at a quantitative understanding of high-energy physics.

AIMS AND LEARNING OUTCOMES

In particular, the learning outcomes are

- present the foundations and the techniques of perturbative quantum field theory;
- introduce the theory of renormalisation;
- provide the students with the necessary knowledge and skills to perform loop calculations with Feynman diagrams;
- present QED at one loop as an example of precision physics;
- provide the students with the necessary knowledge and skills of symbolic programming using mathematica.

PREREQUISITES

The basics of quantum field theory presented in the Theoretical Physics course.

TEACHING METHODS

Blackboard lectures and slides.

SYLLABUS/CONTENT

- Review of covariant perturbation theory. Feynman diagrams. LSZ formalism.
- Quantum Electrodynamics as a gauge theory. An example of a QED process at tree-level. Ward-Takahashi identities.
- An introduction to renormalisation. Loop integrals and their regularisation. Renormalisation schemes.
- Radiative corrections in QED at 1 loop: correction to the fermion propagator. Correction to the vertex function and g-2. Vacuum polarisation.
- Renormalised perturbation theory. Running coupling. An example of a QED process at next-to-leading order.
- The infrared region: soft photons.
- Towards collider phenomenology: Higgs decay into two photons. An introduction to non-Abelian gauge invariance.
- Usage of symbolic computation languages (mathematica) to evaluate Feynman diagrams.

RECOMMENDED READING/BIBLIOGRAPHY

-M. Schwartz: “Quantum Field Theory and the Standard Model”

-M. Maggiore: “A modern introduction to Quantum Field Theory”

-S. Weinberg: “The Quantum Theory of Fields Vol 1”

-M. Peskin and D. Schroeder: “An Introduction to Quantum Field Theory”

-T. Muta “Foundations Of Quantum Chromodynamics: An Introduction To Perturbative Methods In Gauge Theories”

## TEACHERS AND EXAM BOARD

**Office hours:** Please fix an appointment by e-mail.

Exam Board

SIMONE MARZANI (President)

CARLA BIGGIO

STEFANO GIUSTO

NICOLA MAGGIORE

GIOVANNI RIDOLFI (President Substitute)

## LESSONS

TEACHING METHODS

Blackboard lectures and slides.

Class schedule

All class schedules are posted on the EasyAcademy portal.

## EXAMS

EXAM DESCRIPTION

Oral exam about the topics of the syllabus.

ASSESSMENT METHODS

The oral exam will last about 40mins. Every student will be asked to present a topic from the syllabus and questions will be asked in order to assess the student's understanding of the material. During the lectures, students will be given the opportunity to solve problems and exercises, as a means of self-evaluation.